We are using a nine by nine grid and we will move the T is a systematic way to see if wee is able to find a relationship between the numbers across the grid.

23 52

24 57

25 62

The pattern in this table is for the T- Number it is plus one every time and for the T-Total it is plus five every time.

7

8

9

7

N

The nth term = 5N - 63

To find the nth tern I looked at the T - Number value and times it by the gap which is 5 and then subtracted by the first T-number to get the gap which in this case was 63.

Prediction

I predict that when the t - number is 27 the T - total will be 72, and also in an equation the T -number will be 28 and the T-Total will be 77 this is shown in the table below.

26 x 5 - 63 = 67

27 x 5 - 63 = 72

28 x 5 - 63 = 77

2

3

4

5

6

7

8

9

0

1

2

3

4

5

6

7

8

9

20

21

22

23

24

25

26

27

28

29

30

31

32

33

34

35

36

37

38

39

40

41

42

43

44

45

46

47

48

2

3

0

8

2

3

0

8

2

3

4

1

9

3

4

5

2

20

T-Number T-Total

18 34

19 39

20 44

21 49

The pattern in these tables is plus one every time in the T - Number and for the T - Total it is plus five very time.

5

6

7

4

N

The nth term = 5N - 56

To find the nth tern I looked at the T - Number value and times it by the gap which is 5 and then subtracted by the first T-number to get the gap which in this case was 56.

Prediction

I predict that when the t - number is 23 the T - total will be 59, and also in an equation the T -number will be 24 and the T-Total will be 64 this is shown in the table below.

22 x 5 - 56 = 54

23 x 5 - 56 = 59

24 x 5 - 56 = 64

2

3

4

5

6

7

8

9

0

1

2

3

4

5

6

7

8

9

20

21

22

23

24

25

26

27

28

29

30

31

32

33

34

35

36

37

38

39

40

41

42

2

3

0

6

2

3

4

0

7

3

4

5

1

8

4

5

6

2

9

T-Number T-Total

16 31

17 36

18 41

19 46

The pattern with this table is for the T number if plus one every time and for the T total it is plus five every time.

5

6

7

3

N

The nth term = 5N - 49

To find the nth tern I looked at the T - Number value and times it by the gap which is 5 and then subtracted by the first T-number to get the gap which in this case was 49.

Prediction

I predict that when the t - number is 21 the T - total will be 56, and also in an equation the T -number will be 22 and the T-Total will be 61 this is shown in the table below.

20 x 5 - 49 = 51

21 x 5 - 49 = 56

22 x 5 - 49 = 61

2

3

4

5

6

7

8

9

0

1

2

3

4

5

6

7

8

9

20

21

22

23

24

25

26

27

28

29

30

31

32

33

34

35

36

2

3

8

4

2

3

4

9

5

3

4

5

0

6

4

5

6

1

7

T - Number T - Total

14 28

15 33

16 38

The pattern for this table is for the T number is plus one and for the T total is plus five.

4

5

6

1

N

The nth term = 5N - 42

To find the nth tern I looked at the T - Number value and times it by the gap which is 5 and then subtracted by the first T-number to get the gap which in this case was 56.

Prediction

I predict that when the t - number is 18 the T - total will be 48, and also in an equation the T -number will be 19 and the T-Total will be 53 this is shown in the table below.

7 x 5 - 42 = 43

8 x 5 - 42 = 48

9 x 5 - 42 = 53

Formulas

3 x 3 = 19 + (5 x (r-8)

8 x 8 = 34 + (5 x (r-18)

9 x 9 = 37 + (5 x (r - 22)

0 x 10 = 40 + (5 x (r-22)

1 x 11 = 43 + (5x (r-24)

2 x 12 = 46 + (5 x (r-26)

These grids are to work out certain sizes; if you want to work out any size grin you can use the formula below.

(19 + 3 x (r - 3) + (5 x *t - 2 x (T + 1)

What I found out

In this investigation I have found out that this formula above will work out the sizes for any size grid.

Maths Coursework